Buckling of elastically restrained nonlocal carbon nanotubes under concentrated and uniformly distributed axial loads

Buckling of elastically restrained carbon nanotubes is studied subject to a combination of uniformly distributed and concentrated compressive loads. Governing equations are based on the nonlocal model of carbon nanotubes. Weak formulation of the problem is formulated and the Rayleigh quotients are o...

Full description

Saved in:
Bibliographic Details
Published inMechanical sciences (Göttingen) Vol. 10; no. 1; pp. 145 - 152
Main Authors Robinson, Mouafo Teifouet Armand, Adali, Sarp
Format Journal Article
LanguageEnglish
Published Gottingen Copernicus GmbH 26.04.2019
Copernicus Publications
Subjects
Axial loads
Carbon
Carbon nanotubes
Chebyshev approximation
Elastic buckling
Elastic restraints
Mathematical models
Mechanical properties
Nanotubes
Polynomials
Quotients
Ritz method
Stress concentration
Online AccessGet full text
ISSN2191-916X
2191-9151
2191-916X
DOI10.5194/ms-10-145-2019

Cover

Abstract Buckling of elastically restrained carbon nanotubes is studied subject to a combination of uniformly distributed and concentrated compressive loads. Governing equations are based on the nonlocal model of carbon nanotubes. Weak formulation of the problem is formulated and the Rayleigh quotients are obtained for distributed and concentrated axial loads. Numerical solutions are obtained by Rayleigh–Ritz method using orthogonal Chebyshev polynomials. The method of solution is verified by checking against results available in the literature. The effect of the elastic restraints on the buckling load is studied by counter plots in term of small-scale parameter and the spring constants.
AbstractList Buckling of elastically restrained carbon nanotubes is studied subject to a combination of uniformly distributed and concentrated compressive loads. Governing equations are based on the nonlocal model of carbon nanotubes. Weak formulation of the problem is formulated and the Rayleigh quotients are obtained for distributed and concentrated axial loads. Numerical solutions are obtained by Rayleigh–Ritz method using orthogonal Chebyshev polynomials. The method of solution is verified by checking against results available in the literature. The effect of the elastic restraints on the buckling load is studied by counter plots in term of small-scale parameter and the spring constants.
Audience Academic
Author Robinson, Mouafo Teifouet Armand
Adali, Sarp
Author_xml – sequence: 1
  givenname: Mouafo Teifouet Armand
  surname: Robinson
  fullname: Robinson, Mouafo Teifouet Armand
– sequence: 2
  givenname: Sarp
  orcidid: 0000-0003-1781-1531
  surname: Adali
  fullname: Adali, Sarp
BookMark eNp1Ul1rFTEQDVLBWvvq84JPPmyb7GY_8liL1QsFQS34FmYns5dcd5Oa7EL7753bSmulJoRMTs45SSbzWhyEGEiIt0qeNMro0zmXSpZKN2UllXkhDitlVGlU--Pgr_iVOM55J7m1sqpUcyjWDyv-nHzYFnEsaIK8eIRpui0S5SWBD-QKPmqKjBYIaYihCBDisg6UizU4SgXGgBSYvTAZgmPYjzHN7OI8u_hhvdu58ewxRXD5jXg5wpTp-M98JK4uPn4__1xefvm0OT-7LFF3einHFhvsNZLTIGXVgCLX1l2r-9HxqgXdk6odOtV2lUE0nVQ4GDBNV0scoD4Sm3tfF2Fnr5OfId3aCN7eATFtLSR-8URWkQLZKTkgoK4GDeCM6U1NWNXUomGvd_de1yn-Wjk7dhfXFPj6llOpTSNr3T2ytsCmPoyR84Kzz2jPmr5ueWjJrJNnWNwdzZ7TSaNn_Ing_RMBcxa6Wbaw5mw3374-a44p5pxofHi4knZfLHbO-5CLxe6LhQX6HwH6BRYf93_qp__JfgMW6sVh
CitedBy_id crossref_primary_10_5194_ms_12_451_2021
Cites_doi 10.1016/j.compstruct.2016.01.026
10.1016/j.amc.2015.07.114
10.1016/j.physleta.2011.01.046
10.1016/j.ijengsci.2010.12.006
10.1201/b18461
10.1016/j.matdes.2004.01.003
10.1201/9781420041835
10.1063/1.2833431
10.1007/s12206-011-0711-6
10.1016/j.apm.2015.11.026
10.1007/s00707-014-1195-0
10.1017/CBO9781139136860
10.1016/j.physrep.2016.05.003
10.1177/1687814016686925
10.1016/j.compstruct.2018.07.046
10.4028/www.scientific.net/KEM.471-472.1016
10.1061/(ASCE)EM.1943-7889.0000107
10.1142/S0219455415500157
10.1016/j.ijengsci.2007.04.004
10.1016/j.commatsci.2011.07.040
10.24107/ijeas.362242
10.1007/s13204-013-0202-4
10.1016/j.physleta.2008.07.003
10.1515/jmmm-2016-0158
10.5194/ms-8-299-2017
10.1016/j.cap.2012.06.023
10.1080/15376494.2018.1430263
10.12693/APhysPolA.127.678
10.1016/j.physe.2012.02.022
10.1016/j.compstruct.2012.08.024
10.1007/978-81-322-2047-3_2
10.1061/(ASCE)EM.1943-7889.0001088
10.21275/v5i3.NOV162343
10.1007/978-3-319-01201-8
10.1002/zamm.201200130
10.1201/9780203483534
10.4028/www.scientific.net/AMR.123-125.619
10.24107/ijeas.252144
10.1115/1.4001936
ContentType Journal Article
Copyright COPYRIGHT 2019 Copernicus GmbH
2019. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: COPYRIGHT 2019 Copernicus GmbH
– notice: 2019. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
ISR
8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOA
DOI 10.5194/ms-10-145-2019
DatabaseName CrossRef
Gale In Context: Science
ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central Korea
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic (New)
ProQuest Publicly Available Content
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList CrossRef


Publicly Available Content Database
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ: Directory of Open Access Journal (DOAJ)
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2191-916X
EndPage 152
ExternalDocumentID oai_doaj_org_article_1e1a0710bcac42b4aad99893ec23e6c9
A583658340
10_5194_ms_10_145_2019
GroupedDBID .4S
5VS
8FE
8FG
AAFWJ
AAYXX
ABJCF
ACIWK
ADBBV
AENEX
AFKRA
AFPKN
AHGZY
ALMA_UNASSIGNED_HOLDINGS
ARCSS
BCNDV
BENPR
BGLVJ
CCPQU
CITATION
GROUPED_DOAJ
H13
HCIFZ
IAO
IEA
IGS
ISR
ITC
KQ8
L6V
M7S
OK1
PHGZM
PHGZT
PIMPY
PROAC
PTHSS
RKB
RNS
TUS
BBORY
PMFND
ABUWG
AZQEC
DWQXO
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PUEGO
ID FETCH-LOGICAL-c474t-f6c5c84ced4a0025a1ed637648fd25a6a48e13dcd16729cc9701cb9a95730cba3
IEDL.DBID 8FG
ISSN 2191-916X
2191-9151
IngestDate Wed Aug 27 01:20:59 EDT 2025
Fri Jul 25 11:56:24 EDT 2025
Tue Jun 17 21:01:08 EDT 2025
Tue Jun 10 20:45:49 EDT 2025
Fri Jun 27 04:46:08 EDT 2025
Tue Jul 01 04:10:08 EDT 2025
Thu Apr 24 23:02:29 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License https://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c474t-f6c5c84ced4a0025a1ed637648fd25a6a48e13dcd16729cc9701cb9a95730cba3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0003-1781-1531
OpenAccessLink https://www.proquest.com/docview/2214950347?pq-origsite=%requestingapplication%
PQID 2214950347
PQPubID 2037679
PageCount 8
ParticipantIDs doaj_primary_oai_doaj_org_article_1e1a0710bcac42b4aad99893ec23e6c9
proquest_journals_2214950347
gale_infotracmisc_A583658340
gale_infotracacademiconefile_A583658340
gale_incontextgauss_ISR_A583658340
crossref_primary_10_5194_ms_10_145_2019
crossref_citationtrail_10_5194_ms_10_145_2019
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2019-04-26
PublicationDateYYYYMMDD 2019-04-26
PublicationDate_xml – month: 04
  year: 2019
  text: 2019-04-26
  day: 26
PublicationDecade 2010
PublicationPlace Gottingen
PublicationPlace_xml – name: Gottingen
PublicationTitle Mechanical sciences (Göttingen)
PublicationYear 2019
Publisher Copernicus GmbH
Copernicus Publications
Publisher_xml – name: Copernicus GmbH
– name: Copernicus Publications
References ref13
ref35
ref12
ref34
ref15
ref37
ref14
ref36
ref31
ref30
ref11
ref33
ref10
ref32
ref2
ref1
ref17
ref39
ref16
ref38
ref19
ref18
ref24
ref23
ref45
ref26
ref25
ref20
ref42
ref41
ref22
ref44
ref21
ref43
ref28
ref27
ref29
ref8
ref7
ref9
ref4
ref3
ref6
ref5
ref40
References_xml – ident: ref27
  doi: 10.1016/j.compstruct.2016.01.026
– ident: ref16
  doi: 10.1016/j.amc.2015.07.114
– ident: ref3
  doi: 10.1016/j.physleta.2011.01.046
– ident: ref20
– ident: ref21
  doi: 10.1016/j.ijengsci.2010.12.006
– ident: ref22
  doi: 10.1201/b18461
– ident: ref39
  doi: 10.1016/j.matdes.2004.01.003
– ident: ref40
  doi: 10.1201/9781420041835
– ident: ref26
  doi: 10.1063/1.2833431
– ident: ref24
– ident: ref31
  doi: 10.1007/s12206-011-0711-6
– ident: ref9
  doi: 10.1016/j.apm.2015.11.026
– ident: ref36
  doi: 10.1007/s00707-014-1195-0
– ident: ref7
  doi: 10.1017/CBO9781139136860
– ident: ref23
  doi: 10.1016/j.physrep.2016.05.003
– ident: ref5
  doi: 10.1177/1687814016686925
– ident: ref29
  doi: 10.1016/j.compstruct.2018.07.046
– ident: ref12
  doi: 10.4028/www.scientific.net/KEM.471-472.1016
– ident: ref45
  doi: 10.1061/(ASCE)EM.1943-7889.0000107
– ident: ref32
  doi: 10.1142/S0219455415500157
– ident: ref25
  doi: 10.1016/j.ijengsci.2007.04.004
– ident: ref4
  doi: 10.1016/j.commatsci.2011.07.040
– ident: ref14
  doi: 10.24107/ijeas.362242
– ident: ref6
  doi: 10.1007/s13204-013-0202-4
– ident: ref1
  doi: 10.1016/j.physleta.2008.07.003
– ident: ref2
– ident: ref38
  doi: 10.1515/jmmm-2016-0158
– ident: ref28
  doi: 10.5194/ms-8-299-2017
– ident: ref17
  doi: 10.1016/j.cap.2012.06.023
– ident: ref30
  doi: 10.1080/15376494.2018.1430263
– ident: ref44
– ident: ref42
  doi: 10.12693/APhysPolA.127.678
– ident: ref41
  doi: 10.1016/j.physe.2012.02.022
– ident: ref13
  doi: 10.1016/j.compstruct.2012.08.024
– ident: ref15
  doi: 10.1007/978-81-322-2047-3_2
– ident: ref37
  doi: 10.1061/(ASCE)EM.1943-7889.0001088
– ident: ref19
  doi: 10.21275/v5i3.NOV162343
– ident: ref33
  doi: 10.1007/978-3-319-01201-8
– ident: ref18
– ident: ref8
  doi: 10.1002/zamm.201200130
– ident: ref34
  doi: 10.1201/9780203483534
– ident: ref11
  doi: 10.4028/www.scientific.net/AMR.123-125.619
– ident: ref10
– ident: ref43
  doi: 10.24107/ijeas.252144
– ident: ref35
  doi: 10.1115/1.4001936
SSID ssj0000602215
Score 2.0738134
Snippet Buckling of elastically restrained carbon nanotubes is studied subject to a combination of uniformly distributed and concentrated compressive loads. Governing...
SourceID doaj
proquest
gale
crossref
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
StartPage 145
SubjectTerms Axial loads
Carbon
Carbon nanotubes
Chebyshev approximation
Elastic buckling
Elastic restraints
Mathematical models
Mechanical properties
Nanotubes
Polynomials
Quotients
Ritz method
Stress concentration
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwELYQp3Ko-gB1W1pZVaWeIuL4scmRVkXAoYe2SNys8djhspugza5U_j0zTkC7B8SFW2KPLGcyz8TzjRDfjI1Wh8oU5J2qwkAVC3BlKkjvNLg21HE85fvbnV-Zy2t7vdXqi8-EjfDAI-NOVFLAbjAgoKmCAYiUITQ6YaWTw1y6VzblVjI12mDyTbl9AWmkIo22akRspIDFnCwHtj7KWJIRhtjZ8kgZuP8p85x9ztkb8XoKFuXpuMm3Yi9178TBFoTge7HJP2fpUvatTBQK52_TizvJPTe4_UOKkjL87LIkwir0neyg69ebkAbJFWQriVy62GWY2iihizTM9VpLWiUyri63xOKZ_ySrctFDHA7F1dmvfz_Pi6mVQoFmbtZF69BibTBFAxzmgErRkW0xdRvpzoGpk9IRo3IUbSM281JhaKCxZAEwgD4S-7TZ9EHIxtEkxZW6tlyn6kIdlEMK1BurAVHNRPHATo8Tzjg_78JTvsHs98uBL4n9ntk_E98f6W9HhI0nKX_w23mkYmTsPEDy4id58c_Jy0x85XfrGfui48M1N7AZBn_x948_tbWmgEybkvY0EbU97Z2WGmsViAMMl7VDebxDScqJu9MPIuQn4zB4kkxKS0tt5h9f4ok-iVfMHf7FVbljsb9ebdJnipTW4UtWintdcQ80
  priority: 102
  providerName: Directory of Open Access Journals
Title Buckling of elastically restrained nonlocal carbon nanotubes under concentrated and uniformly distributed axial loads
URI https://www.proquest.com/docview/2214950347
https://doaj.org/article/1e1a0710bcac42b4aad99893ec23e6c9
Volume 10
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwELagvcAB8RSFsrIQEiercfzY5IRa1KVwqFChUm-WPXZ62U3KZlei_74zTnbpHsotiUeWMx7PfH59w9gnbaJRodQCo1MptC-j8LZIAsed8rYJVRxO-Z7bs0v948pcjQtu_XiscuMTs6OOHdAa-VFZEpYvlJ5-ufkjKGsU7a6OKTQes32JkYbsvJp9266xFBYjVE5igONS4rg2cuBtRNiijxY9-SCpDVoKEe3ci0uZvv8hJ50jz-w5ezZCRn489PEL9ii1L9nTe0SCr9g6b9HiI-8anhAQ5xXq-S2nzBuUBCJFjvP8HLg4-GXoWt76tlutQ-o53SNbcqALjG0mq43ctxE_062tBdYSiV2XEmNRyV-0WD7vfOxfs8vZ6e-vZ2JMqCBAT_VKNBYMVBpS1J7AjpcpWvQwumoivlmvqyRVhCgtYm6AelpICLWvDfoBCF69YXvY2PSW8dpiIaJLVRm6rWpDFaQFhOu1UR5AHjCxUaeDkW2c_nfucNZB6neLnh5R_Y7Uf8A-b-VvBp6NByVPqHe2UsSPnT90y2s3Djcnk_QEngJ40GXQ3kecV9YqQamSBazkI_WtIwaMlo7YXPt137vvvy7csakUwjKlC2zTKNR02HasarixgBog0qwdycMdSRyisFu8MSE3uoje_TPod_8vfs-e0H_TFlZpD9nearlOHxAJrcIkm_uE7Z-cnv-8mOT1hDvf_Qh3
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELbK9gAcEE-1UMBCIE5R49jxJgeEWmi1S8sKlVbqzdhjp5fdpGx2Bf1T_EZm8li6h3LrLYlHljOelx_zDWNvVepT6RIVoXdKImUTH1kdhwj1TlpduMy3t3wnenSmvpyn5xvsT58LQ9cqe5vYGGpfAe2R7yYJxfKxVMOPlz8jqhpFp6t9CY1WLI7C1S9cstUfxp9xft8lyeHB6adR1FUViEAN1SIqNKSQKQheWfL4VgSvUc1UVnh801ZlQUgPXmgMPAHyYSzA5TZPURnAWYn93mGbijJaB2xz_2Dy7WS1qxNr9IlN2QS0BAItSSpapEgMlNTurCarJ1SKsknQPtc8YVMw4Ca30Pi6w4fsQRek8r1Wqh6xjVA-ZvevQRc-YcvmUBgfeVXwgCF4syc-veJU64PKTgTPy6psXCUHO3dVyUtbVoulCzWnzLU5B0qZLBt4XM9t6fEz5YnNsBdPeL5UiotafqOO8Gllff2Und0Ks5-xAQ42bDGea2zEeFZmKeXHapc5oQEXCHkqLYDYZlHPTgMdvjn979TgOofYb2Y1PSL7DbF_m71f0V-2yB43Uu7T7KyoCJG7-VDNL0yn4EYEYSlcc2BBJU5Z63Elm8sAiQwasJM3NLeGMDdKutRzYZd1bcbfT8xemkkMBKWKcUwdUVHh2LGrNkcCOUAwXWuUO2uUaBRgvbkXIdMZpdr8U6Hn_29-ze6OTr8em-Px5OgFu0c8oAO0RO-wwWK-DC8xDlu4V53wc_bjtvXtLzxBRLk
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZKkRAcEE9RKGAhEKdo1484yQGhQlm6FFUIqNSbscdOL7tJ2ewK-tf4dczksXQP5dZbEo8sZzwvP-Ybxl7qNKTKS52gd5KJdjIkzoxjgnqnnCl9Hrpbvkfm4Fh_OklPttifIReGrlUONrE11KEG2iMfSUmx_FjpbFT21yK-7E_env1MqIIUnbQO5TQ6ETmM579w-da8me7jXL-ScvLh-_uDpK8wkIDO9DIpDaSQa4hBO_L-TsRgUOV0XgZ8M07nUagAQRgMQgGKbCzAF65IUTHAO4X9XmPXM5UVtPDLJx_X-ztjg96xLaCANkGgTUlFhxmJIZMezRuyf0KnKKUE8nPBJ7alAy5zEK3Xm9xht_twle918nWXbcXqHrt1AcTwPlu1x8P4yOuSRwzG293x2Tmnqh9UgCIGXtVV6zQ5uIWvK165ql6ufGw45bAtOFDyZNUC5QbuqoCfKWNsjr0EQvalolzU8hu1hc9qF5oH7PhKWP2QbeNg4yPGC4ONGNmqPKVMWeNzLwzgUqFIlQMQOywZ2GmhRzqn_51ZXPEQ--28oUdkvyX277DXa_qzDuPjUsp3NDtrKsLmbj_Ui1Pbq7oVUTgK3Dw40NJr5wKuaQsVQapoADt5QXNrCX2jIjk-daumsdNvX-1emisMCZUe45h6orLGsWNXXbYEcoAAuzYodzco0TzAZvMgQrY3T439p0yP_9_8nN1ALbOfp0eHT9hNYgGdpEmzy7aXi1V8igHZ0j9rJZ-zH1etan8BykpHiQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Buckling+of+elastically+restrained+nonlocal+carbon+nanotubes+under+concentrated+and+uniformly+distributed+axial+loads&rft.jtitle=Mechanical+sciences+%28G%C3%B6ttingen%29&rft.au=Robinson%2C+Mouafo+Teifouet+Armand&rft.au=Adali%2C+Sarp&rft.date=2019-04-26&rft.pub=Copernicus+GmbH&rft.issn=2191-9151&rft.volume=10&rft.issue=1&rft.spage=145&rft_id=info:doi/10.5194%2Fms-10-145-2019&rft.externalDBID=ISR&rft.externalDocID=A583658340
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2191-916X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2191-916X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2191-916X&client=summon